# Newtons Laws

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```					Newton’s Laws
Forces and Motion
Laws of Motion
 formulated by Issac Newton in the
late 17th century
 written as a way to relate force and
motion
 Newton used them to describe his
observations of planetary motion.
History
   Aristotle was an ancient Greek philosopher
   Based on his observations the common
belief was that in order for an object to
continue moving, a force must be exerted
in the direction of the motion
   This lasted until Issac Newton proposed
his “Laws of Motion” based on
observations made of bodies free from
earth’s atmosphere.
Newton’s 1st Law
Inertia

An object at rest will stay at rest, and
an object in motion will stay in
motion at constant velocity unless
acted on by an unbalanced force.
This statement contradicted Aristotle’s teaching and was
considered a radical idea at the time. However, Newton
proposed that there was, in fact, an unrecognized force of
resistance between objects that was causing them to stop
in the absence of an applied force to keep them moving.
This new unseen resistance force became known as
“friction”.
Newton’s 2nd Law
Fnet = ma

If an unbalanced force acts on a
mass, that mass will accelerate in the
direction of the force.
Since 8N is greater than 2N,
2N                  8N         the unbalanced force (6N) is to
the right so the acceleration is
to the right.
a

Newton’s 1st Law says that without an unbalanced
force objects will remain at constant velocity
(a=0)…so it seems logical to say that if we apply a
force we will see an acceleration.
Newton’s 3rd Law
Action - Reaction

For every action force there is an
equal and opposite reaction force.
Example: If you punch a wall with your fist in anger,
the wall hits your fist with the same force.
That’s why it hurts!

Action-reaction forces cannot balance each other
out because they are acting on different objects.
The forces acting on an object determine their
motion.
Fnet
Fnet  ma        or      a
m

   Acceleration and net force are directly
related. If Fnet doubles, acceleration doubles.

   Acceleration and mass are indirectly related.
If m doubles, acceleration is half as much.
A Force is…
 Measured in Newtons (N) in the
metric (SI) system and pounds (lbs)
in the English system
 A vector quantity requiring magnitude
and direction to describe it
 Represented by drawing arrows on a
diagram
Types of Forces
(that we will study now – there are many more)

   Weight - force of gravity
   Normal force – surface pushing back
   Friction - resistance force that opposes motion
   Applied force - force you exert, push or pull
   Tension - applied through a rope or chain
   Net force – total vector sum of all forces
   Balanced forces – equal and opposite forces
   Unbalanced forces – not equal and opposite
Weight
The force of gravity acting on a mass.
Weight always acts down!

Weight = mass (kg) * acceleration due to gravity

Fg  W  m  g
Weight is a force…so this is a special case
of F=ma and the unit is a Newton.
Mass is…
 The amount of matter in an object.
 Measured in kilograms.

 NOT a force.

 The same at any location, even on
another planet. Not influenced by
gravity.
Normal Force (FN)
   Defined as the force of a surface pushing
back on an object.
   Always directed perpendicular to the
surface.
   This is a contact force. No contact…no
normal force.
   NOT always equal to weight.
FN
Examples:                   FN   W
a
l
l
Table
Friction
   A resistance force usually caused by two
surfaces moving past each other.
   Always in a direction that opposes the
motion.
   Measured in Newtons.
   Depends on surface texture and how hard
the surfaces are pressed together.
   Surface texture determines the coefficient
of friction (μ) which has no units.
   Normal force measures how hard the
surfaces are pressed together.
Types of friction
   Static friction is the force an object must
overcome to start moving.
   Kinetic friction is the force an object must
overcome to keep moving.

Static friction is always greater
than kinetic friction!
Calculating the Force of Friction

f   FN
Where f is the force of friction, μ is the coefficient of
friction, and FN is the normal force. μ has no units!

For kinetic friction:   f k   k FN
For static friction:
f s  s FN
May the   Net Force be with you
   Total force acting on an object
   Vector sum of all the forces
   The unbalanced force referred to in Newton’s
Law of Motion
   Net force is equal to the mass of an object times
the acceleration of that object.

Fnet   F                 Fnet  ma
Net force can be found by finding
the sum of the force vectors or by
mass times acceleration.
Example using mass times acceleration:
Find the net force for a 20 kg object that
is being accelerated at 3 m/s2 .
Fnet  ma
Fnet  20kg (3 m s )2

Fnet  60 N
If acceleration is not given, use the
kinematics equations to find “a” first:

v f  vi
a
t
d  vi t    1
2 at 2
vi  v f
d                 (t )
2
vi 2  v f 2  2ad
Or conversely you may have to
use the Fnet formula to get
acceleration and then the
kinematics equations to find
t, d, vi, or vf.
Finding net force using sum of the
force vectors:
Example 1                                             Example 2

10 N              30 N                                      50 N

Fnet
Fnet= 20 N
=10 N
40 N
Example 3

15 N                                                        Must draw vectors tip to
5N                            14 N               tail first before solving:
12 N
Fnet
=                                                   14 N
7N                                                                         Ө
2N                              7N
6N                                                           7N

Fnet 2 = 14 2 + 7   2   Ө = tan-1 (14 / 7)
Fnet = 15.7 N            Ө = 63.4º
Force Diagrams
   Force diagrams must include the object
and all forces acting on it.
   The forces must be attached to the object.
   No other vectors may be attached to the
object.
   Components of forces, axis systems,
motion vectors and other objects or
surfaces may be included in force
diagrams.
   Put the mass in the object box.
Force Diagram
Problem: A 10 kg crate with an applied force of 100 N slides across a
warehouse floor where the coefficient of static friction is 0.3 between
the crate and the floor. What is the acceleration of the crate?

FN

f = μFN                             Fapplied = 100 N
10 kg

Weight = Fg = (10 kg)*(9.81m/s2)
To Solve the Problem
Now that you have the force diagram!
Problem: A 10 kg crate with an applied force of 100 N slides across a
warehouse floor where the coefficient of static friction is 0.3 between
the crate and the floor. What is the acceleration of the crate.

FN

f = μFN
10 kg
Fapplied = 100 N
a

Weight = Fg = (10 kg)*(9.81m/s2)

Write the Newton’s 2nd Law equation for the x- and y- directions.
This time we will use both sum of forces and ma as Fnet.

Fnet , x :  Fx  max                           Fnet , y :  Fy  ma y
Fa  f  max                                    FN  Fg  ma y

Now plug in what you know and solve for what you don’t.
Solving the Problem:
Problem: A 10 kg crate with an applied force of 100 N slides across a
warehouse floor where the coefficient of static friction is 0.3 between
the crate and the floor. What is the acceleration of the crate.

FN

f = μFN
10 kg
Fapplied = 100 N
a

Weight = Fg = (10 kg)*(9.8m/s2)

Fnet , x   Fx  max                                                Fnet , y   Fy  ma y
Fa  f  max                                                         FN  Fg  ma y
Fa   FN  max
FN  98 N  0
100 N  0.3(98 N )  10kg ( ax )
FN  98 N
70.6 N  10kg ( ax )                                                                          Fnet   Fx  max

ax  7.06 m s 2

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